Leading logarithms for the nucleon mass

TL;DR

This paper analyzes the leading logarithm behavior of the nucleon mass within heavy baryon chiral perturbation theory, providing exact calculations up to four loops and conjectures for all orders, enhancing understanding of quantum corrections in nucleon mass calculations.

Contribution

It presents the first exact multi-loop calculations of leading logarithms for the nucleon mass and proposes an all-order conjecture, advancing theoretical precision in chiral perturbation theory.

Findings

Exact four-loop leading logarithm results for nucleon mass.

All-order conjecture for leading logarithm behavior.

Calculation of coefficients for fractional power terms.

Abstract

Within the heavy baryon chiral perturbation theory approach, we have studied the leading logarithm behaviour of the nucleon mass up to four-loop order exactly and we present some results up to six-loop order as well as an all-order conjecture. The same methods allow to calculate the main logarithm multiplying the terms with fractional powers of the quark mass. We calculate thus the coefficients of $m^{2n+1}\log^{(n-1)}(\mu^2/m^2)$ and $m^{2n+2}\log^n(\mu^2/m^2)$, with $m$ the lowest-order pion mass. A side result is the leading divergence for a general heavy baryon loop integral.